Question

In the figure below, ACDE is similar to AFGH.

D
G
11
8
C
5 E
2X+4
F
H
If the perimeter of AFGH is 48 units, find the value of x.

Answer 1

6

Explanation:

`\triangle CDE \sim \triangle FGH`

`(P(\triangle CDE) )/(P(\triangle FGH)) =(CD)/(GH)`

(Area of similar triangle theorem)

`(11+8+5)/(48) =(8)/(2x +4)`

`(24)/(48) =(8)/(2x +4)`

`(1)/(2) =(8)/(2x +4)`

`2x + 4 = 2* 8`

`2x + 4 =16`

`2x =16-4`

`2x =12`

`x =(12)/(2)`

`x = 6`

Answer 2

6

Explanation:

`1)\ P_1 = 11 + 8 + 5 = 24\ units`

`2)\ 2x + 4 + y +z = 48`

`3)\ (48)/(24) = 2 => 2x+4 = 2*8`

`4)\ 2x+4 = 2*8 => 2x + 4 = 16 => 2x = 12 => x = 6`